On SAP-rings

Abstract

The rings whose simple right modules are absolutely pure are called right $SAP$-rings. We give a new characterization of right $SAP$ rings, right $V$ rings, and von Neumann regular rings. We also obtain a new decomposition theory of right selfinjective von Neumann regular rings. The relationships between $SAP$-rings, $V$-rings, and von Neumann regular rings are explored. Some recent results obtained by Faith are generalized and the results of Wu-Xia are strengthened.